Learn all Concepts of Chapter 8 Class 10 (with VIDEOS). Check - Trigonometry - Class 10

Last updated at Dec. 24, 2019 by Teachoo

Transcript

Example 2 If ∠ B and ∠ Q are acute angles such that sin B = sin Q, then prove that ∠ B = ∠ Q. Given: sin B = sin Q To prove: ∠ B = ∠ Q Proof: Let’s take two right angle triangles ABC & PQR Since, sin B = sin Q 𝐴𝐶/𝐴𝐵=𝑃𝑅/𝑃𝑄 𝐴𝐶/𝑃𝑅=𝐴𝐵/𝑃𝑄 Let 𝐴𝐶/𝑃𝑅=𝐴𝐵/𝑃𝑄= k So, AC = k PR & AB = k PQ Now, Using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 Now, 𝐵𝐶/𝑄𝑅 = √(𝐴𝐵2 −𝐴𝐶2)/√(𝑃𝑄2 −𝑃𝑅2) 𝐵𝐶/𝑄𝑅= √((𝑘𝑃𝑄)2−(𝑘𝑃𝑅)2)/√(𝑃𝑄2 −𝑃𝑅2) 𝐵𝐶/𝑄𝑅= √(𝑘2 𝑃𝑄2− 𝑘2𝑃𝑅2)/√(𝑃𝑄2 −𝑃𝑅2) 𝐵𝐶/𝑄𝑅= (𝑘√(𝑃𝑄2−𝑃𝑅2))/√(𝑃𝑄2 −𝑃𝑅2) 𝐵𝐶/𝑄𝑅 = k From (1) and (2) 𝐴𝐶/𝑃𝑅 = 𝐴𝐵/𝑃𝑄 = 𝐵𝐶/𝑄𝑅 = k 𝐴𝐶/𝑃𝑅 = 𝐴𝐵/𝑃𝑄 = 𝐵𝐶/𝑄𝑅 Hence, corresponding sides of Δ ABC & Δ PQR are in the same ratio Thus, ∆ ABC ~ ∆ PQR So, ∠ B = ∠ Q Hence proved

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Example 2 Important You are here

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Example 9 Not in Syllabus - CBSE Exams 2021

Example 10 Important Not in Syllabus - CBSE Exams 2021

Example 11 Important Not in Syllabus - CBSE Exams 2021

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.